138 



TREATISE ON ALTERNATING CURRENTS. 



The fundamental equation is of the fourth degree in c and ?', 

 and is symmetrical with respect to the axes (since e and i occur 

 \vith even exponents only). 



The curves in the first and third quadrants represent the con- 

 dition of affairs when the machine is running as a generator, since 



FIG. 40. 



in these quadrants c and i have always the same sign. In the 

 second and fourth quadrants the machine is running as a motor. 

 The symmetry of the curves renders a detailed consideration of the 

 second quadrant sufficient. 



By squaring and transposing the fundamental equation, we can 

 put it in the form 



= 



Solving this as a quadratic equation in i 2 , we get 



+ 1 



- ZrPw 



Now, i must be real, therefore i 2 must be real and positive, 



